Massive Neutrinos

Abstract

The mass term connects a left-handed field to its right-handed partner, i.e., it is the term that flips the chirality of a particle. There are two possible mass terms, the Dirac mass term,

$$ m\left( {{{\bar \psi }_R}{\psi _L} + h.c.} \right), $$

(6.1)

and the Majorana mass term,

$$M\left( {\bar \psi _L^c{\psi _L} + h.c.} \right) $$

(6.2)

, where \({\psi ^c} = C{\gamma ^0}{\psi ^*}\) is the charge-conjugated field of Ψ and \(\psi _L^c \equiv {\left( {{\psi _L}} \right)^c} = \frac{{\left( {1 + {\gamma _5}} \right)}}{2}{\psi ^c}\)
has right-handed chirality. The former is the term \(m\bar \psi \psi \) that gives a mass to quarks and charged leptons. The latter obviously violates lepton-number conservation by two units and makes a particle and its antiparticle indistinguishable. (The classical experiment by Davis [94], who showed that \(\bar \nu + {}^{37}Cl \to {}^{37}A + {e^ - }\) does not take place, is interpreted as a virtue of the right-handed helicity of v̄ this test does not preclude the possibility of the Majorana neutrino.) As discussed in Sect. 5.1, a Major and mass term is allowed only for the neutrino. When neutrinos have a Majorana mass term, they are generally called “Majorana neutrinos.” This terminology is not quite accurate and a more precise definition is given in this chapter.